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The reduced cubic equation $y^3 + 3py +2q = 0$ has one real and two complex
solutions when $D = q^2 + p^3 > 0$. These are given by Cardan's formula as
\begin{equation} y_1 = u + v \end{equation}
\begin{equation} y_2 = -\frac{u+v}{2} + \frac{i}{2}\sqrt{3}(u-v) \end{equation}
\begin{equation} y_3 = -\frac{u+v}{2} - \frac{i}{2}\sqrt{3}(u-v) \end{equation}
where
\[ u = \sqrt[3]{-q + \sqrt{q^2+p^3}},\qquad v = \sqrt[3]{-q - \sqrt{q^2+p^3}} \]
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